13. Determine whether the alternating series is absolutely converg ally convergent, or divergent. Justify your answer. Turn in at least two problems. (a) n=1 (-1)" 5n+1 (b) n= (-1)" n² 1 (c)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please solve 13 a) determine whether the alternating series is absolutely convergent, conditionally convergent or divergent
n=
(a)
(a)
(a)
13. Determine whether the alternating series is absolutely convergent, condition-
ally convergent, or divergent. Justify your answer.
Turn in at least two problems.
n=1
1
+8
n=1
(-1)"
5n+1
5n
(n + 1)!
(b) Σ
Σ(1)
2n² + 1
(b)
14. Use the Ratio Test to determine whether the series is convergent or diver
gent. Turn in at least two problems.
n
4"
3n 2
(b)
WI
-1)"
1
n
(c) Σ m² + 1
n=1
n
5n
(c) Σ cos(n)
n=1
∞
(b) Σ
15. Use the Root Test to determine whether the series is convergent or div
gent. Turn in at least one problem.
(c)
n=1
12n + 1
5n² + 1.
n=1
+1)"
(-1)^3n
2nn3
Transcribed Image Text:n= (a) (a) (a) 13. Determine whether the alternating series is absolutely convergent, condition- ally convergent, or divergent. Justify your answer. Turn in at least two problems. n=1 1 +8 n=1 (-1)" 5n+1 5n (n + 1)! (b) Σ Σ(1) 2n² + 1 (b) 14. Use the Ratio Test to determine whether the series is convergent or diver gent. Turn in at least two problems. n 4" 3n 2 (b) WI -1)" 1 n (c) Σ m² + 1 n=1 n 5n (c) Σ cos(n) n=1 ∞ (b) Σ 15. Use the Root Test to determine whether the series is convergent or div gent. Turn in at least one problem. (c) n=1 12n + 1 5n² + 1. n=1 +1)" (-1)^3n 2nn3
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